32-year-old Schiller, who ran a surfing school on the island, was in the waters off the Boucan Canot beach with other surfers when the attack happened.
“The attack was sudden,” said one of the witnesses, according to AFP. Other witnesses on the beach said they saw the surfer in difficulty and then a pool of blood.
The other surfers managed to put the victim’s body onto his surfboard but it was carried away by waves. Emergency services were mobilized but the body had still not been found by Tuesday morning.
The attack is the fourth by a shark since the start of the year on the island. In June, a 31-year-old man was killed while surfing in the same waters.
Schiller was French bodyboarding champion in 1994 and European team champion in 1995. He started his surf school in 2008 and launched a line of surfing wear in 2009.
La Reunion, which sits to the east of Madagascar in the Indian ocean, is considered an ‘overseas department’ of France with a population of about 800,000.
Water sports will be banned from Tuesday in areas lying up to 300 metres from red flags.